Fitting model with three latent variables and 16 ordinal and four continuous indicators

Thanks for your reply.
I'd avoid imputing data if at all possible. However, it might be necessary the estimates vary considerably between WLS and ML.
The approach you describe sounds interesting. I couldn't really find much on WLSMV, from what I could figure out, MPlus uses this method by default for categorical variables. However, I couldn't really figure out how to implement it in OpenMx. Do you have any articles, tutorials, or example scripts you can recommend?

To add to my previous comment, I've been testing a partial model with fewer ordinal variables (to be able to get ML estimates). One thing I noticed is that both ML and WLS produced inconsistent estimates. If I rerun the exact same model without any modifications, I will still get very varying estimates. In comparison DWLS estimates seem to produce far more consistent and reasonable outputs (see attachment).
How does WLSMV differ from the "DWLS" option in mxFitFunctionWLS()?
I've been trying to find some information on WLSMV, and [this comment](https://groups.google.com/g/lavaan/c/Nymu7jmVUk8/m/Su_dhLMgBwAJ) claims "WLSMV is just a keyword in the Mplus language that simultaneously requests the DWLS estimator and a mean- and variance-adjusted (MV) chi-squared test statistic. (...) lavaan implements the same as Mplus describes in its technical literature (available on their website), which can be requested using the arguments:

lavaan(..., estimator = "DWLS", se = "robust.sem", test = "scaled.shifted") "

Is there a similar way for implementing WLSMV in OpenMx? I am also curious as to how this fit function treats missing data. Unless it's imputed, I gather it will use listwise deletion?

[Update:]
According to the [OpenMx v. 2.11 release logs](https://openmx.ssri.psu.edu/node/4413), WLSMV was implemented in this update ( mxFitFunctionWLS() ). Am I correct in assuming that this is the same as DWLS in OpenMx (mxFitFunctionWLS(type = "DWLS"))?

This lead me to the latter half of your comment: "(...) WLSMV is better for your application, where the correlations have initially been estimated by ML (...). Could you elaborate what you mean by that or how to proceed? Should I build partial models or a CFA estimated by ML, and use these estimates in a full model estimated by WLSMV/DWLS? In such case, I am wondering how to proceed. I already restricted all means and variances of the ordinal indicators and their latent variables to 1. (Only the continuous indicators and their latent variable are freely estimated means and variances.)

According to [Kline (2016, pp. 301)](https://books.google.no/books?id=Q61ECgAAQBAJ&lpg=PP1&ots=jFin3pz9sg&dq=kline%202016%20principles%20and%20practice%20structural%20equation%20modeling&lr&pg=PP1#v=onepage&q=kline%202016%20principles%20and%20practice%20structural%20equation%20modeling&f=false), "a standardized solution where all variables have unit variance (1.0), standardized pattern coefficients for simple indicators (they depend on a single factor) are estimated Pearson correlations. In this case, squared standardized pattern coefficients are proportions of explained variance. If a standardized coefficient is .80, for example, then the factor explains $.80^2 = .64$, or 64.0% of the observed variance of that simple indicator.".

If this is the case, for any latent variable with only simple indicators, all pattern coefficients $\lambda_i$ should be
$$
0 \leq \lambda_i \leq 1 ,
$$ and
$$
\sum_{i=1}^{n} \lambda_i^2 = 1 ,
$$
which they clearly are not. Should I constrain my model to meet these criteria for a proper standardized solution?